$2\mathrm{.}4-13$ A tube structure is acted on by loads at $B$ and $D,$ as shown in the figure. The tubes

are joined using two flange plates at $C$ that are bolted together using six $0\mathrm{.}5-in.$ diameter

bolts.

a$.$ Derive formulas for the reactions $R_A$ and $R_E$ at the ends of the bar.

Answer:

$R_A=2\frac{P}{3},R_E=-5\frac{P}{3}$

b$.$ Determine the axial displacements ${}_B,{}_C,$ and ${}_D$ at points $B,C,$ and $D,$

respectively.

Answer:

${}_B=-\frac{LP}{6EA},{}_C=-\frac{LP}{6EA},{}_D=\frac{5LP}{6EA}$

c$.$ Draw an axial$-$displacement diagram $($ADD$)$ in which the abscissa is the distance

$x$ from support A to any point on the bar and the ordinate is the horizontal

displacement $$ at that point.

Answer:

${}_{\text{m}\text{a}\text{x}}=\frac{5LP}{6EA}(to$ the right$),{}_A={}_E=0$

d$.$ Find the maximum value of the load variable $P$ if allowable normal stress in the

bolts is $14$ ksi $.$

Answer:

$P_{\text{m}\text{a}\text{x}}=12\mathrm{.}37$kips

Problem $2\mathrm{.}4-13$